Take a look at SFF PCs

SFF, or small form factor, is what is behind those tiny, cube-like PCs that can be carried around very, very easily. They don't hold much - no RAID arrays or massive graphics cards or multiple DVD writers - but then you don't go with SFF for that. And besides, with the kinds of capacities we are seeing in HDDs and RAM recently, limiting a PC to a single HDD or having a mobo with only 2 DIMM slots isn't potentially the crime it used to be.

Extremetech have an article on a small form factor roundup, where they discuss some of the SFF kit that is around, and what's possible with it. There's plenty here to guide you into building that LAN party cube.